2110014002
Level:
A
In one of the pictures given below is not a graph of a part of a geometric sequence. Choose this graph.
Geometric sequences
1003112804
Level:
B
The third term of a geometric sequence is \( -5 \) and the eighth term is \( -5 \). \( s_5 \) is the sum of the first five terms and \( q \) is the common ratio of this sequence. Choose the formula which is not valid for this sequence:
\( s_5=-5\cdot\frac{q^5-1}{q-1} \)
\( s_5=-25 \)
\( s_5=5\cdot a_1 \)
\( s_5=5\cdot a_3 \)
\( s_5=5\cdot(-5) \)
1003112806
Level:
B
The sum of the first four terms of a geometric sequence is \( 0 \) and the first term equals \( 2 \). Choose the correct formula to find the eighth term.
\( a_8 = 2\cdot (-1)^7 \)
\( a_8 = 2\cdot (1)^7 \)
\( a_8 = 2\cdot 2 \)
\( a_8 = \frac02 \)
\( a_8 = 2\cdot (-2) \)
1003112807
Level:
B
The sum of the first two terms of a geometric sequence is \( 28 \) and its first term equals \( 2 \). Which of the following statements about its common ratio \( q \) is not valid?
\( q \) is an even number.
\( q > 10 \)
\( q < 28 \)
\( q \) is prime number.
\( q \) is a divisor of \( 26 \).
1003112808
Level:
B
The first term of a geometric sequence is \( 15 \) and the common ratio is \( -1 \). Find the sum of the first \( 10 \) terms of this sequence.
\( 0 \)
\( 15 \)
\( -15 \)
\( 150 \)
\( -150 \)
1003112810
Level:
B
The sum of the first \( n \) terms of a geometric sequence is \( -5 \), the common ratio is \( -2 \) and the first term equals \( 1 \). Find \( n \).
\( 4 \)
\( 3 \)
\( 5 \)
\( 6 \)
\( 2 \)
1003112812
Level:
B
The sum \( s_3 \) of the first three terms of a geometric sequence is \( 21 \) and its common ratio is \( -2 \). Which of the following (in)equalities is true for the first term of the sequence?
\( a_1 > 0 \)
\( a_1 < 0 \)
\( a_1 = 0 \)
\( a_1 < a_2 \)
\( a_1 > s_3 \)
1003134602
Level:
B
The sum of the second and the third term of a geometric sequence is $6\log3$ and the common ratio is $2$. Find the sum of the first three terms.
$7\log3$
$2\log3^6$
$2\log6$
$\log9$
$3\log6$
1003134603
Level:
B
The sum of the first five terms of a geometric sequence is less than $1$ and the common ratio is $10$. Determine all possible values of the first term.
$ a_1 < \frac1{11111}$, $a_1\in\mathbb{R}$
$ -\frac1{10^5} < a_1 < \frac1{10^5}$, $a_1\in\mathbb{R}$
$a_1 < \frac1{99999}$, $a_1\in\mathbb{R}$
$a_1 < 10^{-4}$, $a_1\in\mathbb{R}$
$a_1 < 10^{-5}$, $a_1\in\mathbb{R}$
1003134604
Level:
B
Find the $5$th term of a geometric sequence $\{a_n\}_{n=1}^{\infty}$, where $a_1\cdot a_3\cdot a_5=x^3$, and $\frac{a_4}{a_2} =y^4$.
$xy^4$
$\frac x{y^4}$
$\frac x{y^2}$
$x$
$xy^2$